Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 955 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.If 6 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹15 (b) ₹90 (c) ₹27 (d) ₹20
2. 2.₹35 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹21 (c) ₹7 (d) ₹14
3. 3.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 17 days (c) 7 days (d) 28 days
4. 4.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹81 (b) ₹108 (c) ₹27 (d) ₹135
5. 5.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 21 days (d) 13 days
6. 6.If 4 kites cost ₹36, how much do 2 kites cost? (a) ₹27 (b) ₹72 (c) ₹34 (d) ₹18
7. 7.₹216 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹216 (b) ₹24 (c) ₹192 (d) ₹108
8. 8.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹344 (b) ₹43 (c) ₹301 (d) ₹86
9. 9.If 6 mangoes cost ₹48, how much do 3 mangoes cost? (a) ₹45 (b) ₹144 (c) ₹32 (d) ₹24
10. 10.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 17 days
11. 11.If 8 mangoes cost ₹176, how much do 2 mangoes cost? (a) ₹66 (b) ₹352 (c) ₹170 (d) ₹44
12. 12.If 4 notebooks cost ₹24, how much do 9 notebooks cost? (a) ₹60 (b) ₹29 (c) ₹54 (d) ₹216
13. 13.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 25 days (c) 17 days (d) 13 days
14. 14.₹672 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹432 (d) ₹336
15. 15.If 4 pens cost ₹40, how much do 11 pens cost? (a) ₹120 (b) ₹110 (c) ₹440 (d) ₹47
16. 16.If 3 pens cost ₹66, how much do 8 pens cost? (a) ₹528 (b) ₹176 (c) ₹71 (d) ₹198
17. 17.If 8 mangoes cost ₹120, how much do 11 mangoes cost? (a) ₹180 (b) ₹123 (c) ₹1320 (d) ₹165
18. 18.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹187 (b) ₹238 (c) ₹136 (d) ₹34
19. 19.If 2 notebooks cost ₹26, how much do 11 notebooks cost? (a) ₹286 (b) ₹35 (c) ₹156 (d) ₹143
20. 20.₹78 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹6 (b) ₹54 (c) ₹39 (d) ₹24
21. 21.₹484 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹352 (b) ₹132 (c) ₹242 (d) ₹44
22. 22.If 4 mangoes cost ₹20, how much do 3 mangoes cost? (a) ₹20 (b) ₹60 (c) ₹15 (d) ₹19
23. 23.4 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 14 days (d) 2 days
24. 24.If 8 kites cost ₹24, how much do 7 kites cost? (a) ₹23 (b) ₹21 (c) ₹24 (d) ₹168
25. 25.₹186 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹186 (b) ₹93 (c) ₹155 (d) ₹31
26. 26.8 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 33 days (b) 7 days (c) 32 days (d) 17 days
27. 27.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹117 (b) ₹13 (c) ₹104 (d) ₹65
28. 28.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 4 days (d) 2 days
29. 29.If 4 pens cost ₹64, how much do 8 pens cost? (a) ₹512 (b) ₹144 (c) ₹68 (d) ₹128
30. 30.If 8 pens cost ₹160, how much do 4 pens cost? (a) ₹156 (b) ₹640 (c) ₹100 (d) ₹80
31. 31.If 4 mangoes cost ₹20, how much do 2 mangoes cost? (a) ₹40 (b) ₹10 (c) ₹15 (d) ₹18
32. 32.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 35 days (c) 36 days (d) 5 days
33. 33.If 2 kites cost ₹40, how much do 3 kites cost? (a) ₹80 (b) ₹120 (c) ₹60 (d) ₹41
34. 34.If 6 pens cost ₹60, how much do 10 pens cost? (a) ₹110 (b) ₹600 (c) ₹64 (d) ₹100
35. 35.If 8 pens cost ₹152, how much do 9 pens cost? (a) ₹153 (b) ₹190 (c) ₹171 (d) ₹1368
36. 36.₹45 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹5 (b) ₹41 (c) ₹45 (d) ₹40
37. 37.₹176 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹132 (b) ₹44 (c) ₹88 (d) ₹176
38. 38.If 2 mangoes cost ₹12, how much do 9 mangoes cost? (a) ₹108 (b) ₹19 (c) ₹60 (d) ₹54
39. 39.If 9 kites cost ₹54, how much do 2 kites cost? (a) ₹47 (b) ₹108 (c) ₹12 (d) ₹18
40. 40.₹286 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹88 (b) ₹143 (c) ₹198 (d) ₹22

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